Harmonic measure and radial projection

Source abstract

Among all curves in the closed unit disk that meet every radius, there is one, γ 0 {\gamma _0} , whose harmonic measure at the origin is minimal. We give an explicit description of γ 0 {\gamma _0} and compute its harmonic measure. We also give a quadratically convergent algorithm to compute the harmonic measure of one side of a rectangle at its center.